Determining the Specific Heat Capacity of Air by yurtgc548

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									Determining the Specific Heat 
      Capacity of Air
      Contents
Ⅰ: Aim
Ⅱ: Introduction
Ⅲ: Theory
Ⅳ: Experimental Process
Ⅴ: Instruments and Data Table
Ⅰ: Aim

• To measure the specific heat ratio of 
  air by the method of adiabatic 
  expansion.
• To learn how to use the temperature 
  sensor and the pressure sensor. 
Ⅱ:Introduction
• The heat capacity ratio or adiabatic index or ratio of
  specific heats, is the ratio of the heat capacity at
  constant pressure (CP) to heat capacity at constant
  volume (CV). It is sometimes also known as the
  isentropic expansion factor and is denoted by γ
  (gamma).



    where, C is the heat capacity or the specific heat
  capacity of a gas, suffix P and V refer to constant
  pressure and constant volume conditions respectively.
 Ideal gas relations
• For an ideal gas, the heat capacity is constant
  with temperature. Accordingly we can express
  the enthalpy as H = CPT and the internal
  energy as U = CVT. Thus, it can also be said
  that the heat capacity ratio is the ratio between
  the enthalpy to the internal energy:
Ideal gas relations
• Furthermore, the heat capacities can be
  expressed in terms of heat capacity ratio ( γ )
  and the gas constant ( R ):

                 and


So:
 Relation with degrees of freedom
• The heat capacity ratio ( γ ) for an ideal gas can be
  related to the degrees of freedom ( f ) of a molecule by:


• Thus we observe that for a monatomic gas, with three
  degrees of freedom:


• while for a diatomic gas, with five degrees of freedom
  (at room temperature):
E.g. 
• The terrestrial air is primarily made up of diatomic 
  gasses (~78% nitrogen (N2) and ~21% oxygen 
  (O2)) and, at standard conditions it can be 
  considered to be an ideal gas. A diatomic 
  molecule has five degrees of freedom (three 
  translational and two rotational degrees of 
  freedom). This results in a value of 
Ratio of Specific Heats for 
  some common gases 
         Gas             Ratio of Specific Heats
   Carbon Dioxide                 1.3
       Helium                     1.66
      Hydrogen                    1.41
Methane or Natural Gas            1.31
       Nitrogen                   1.4
       Oxygen                     1.4
     Standard Air                 1.4
 One Standard Atmosphere
Common Pressure Units frequently used as
    alternative to "one Atmosphere"
• 76 Centimeters (760 mm) of Mercury 
• 10.332 Meters of Water 
• 101.33 Kilopascal 
Note: Standard atmosphere is a pressure defined as 
    101'325 Pa and used as unit of pressure (symbol: 
    atm). 
     The original definition of “Standard Temperature 
    and Pressure” (STP) was a reference temperature 
    of 0 °C (273.15 K) and pressure of 101.325 kPa (1 
    atm). 
Ⅲ:Theory
•   Ideal gas law
     – The state of an amount of gas is determined by its
         pressure, volume, and temperature according to the
         equation:
          
    where
     P  is the absolute pressure of the gas,
     V  is the volume of the gas,
     n is the number of moles of gas,
     R  is the universal gas constant,
     T   is the absolute temperature.
The value of the ideal gas constant, R, is found to be as 
    follows.
     R = 8.314472J·mol−1·K−1
Calculations
  Process           Constant       Equation
Isobaric process     Pressure      V/T=constant

Isochoric process     Volume       P/T=constant

   Isothermal 
                    Temperature    PV=constant
     process
   Isentropic 
    process                        PVγ=constant
  (Reversible         Entropy     Pγ-1/Tγ=constant
    adiabatic                     TVγ-1=constant
    process) 
Isotherms of an ideal gas 

                             T: high




           T: low
Ⅳ: Experimental process

       Adiabatic       Isochoric process 
       expansion           (pressure 
                           increase)

Ⅰ(P1,T0)        Ⅱ(P0,T1)        Ⅲ(P2,T0)
Calculations
Adiabatic expansion.Ⅰ(P1,T0)----Ⅱ(P0,T1)




                               Equation 1
Calculations
Isochoric process (pressure increase).
Ⅱ(P0,T1)------Ⅲ(P2,T0)




                                 Equation 2
Calculations
Through equation 1 and 2




                           Equation 3
Ⅴ:Instruments and data table
Testing Instrument
Sensitivity
• The Pressure Sensor:20mV/kPa




• The Temperature Sensor:5mV/K
Data table
    P0(kPa         ΔP1      P1     ΔP1   P2 (kPa
             T0                                    γ
       )          (mV )   (kPa)   (mV)      )

1

2

3
    101.30
4

5

6
Result

								
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